Classifying rotationally-closed languages having greedy universal cycles (Q1732029)

Summary: Let \(\mathbf{T}(n,k)\) be the set of strings of length \(n\) over the alphabet \(\Sigma=\{1,2,\dots,k\}\). A universal cycle for \(\mathbf{T}(n,k)\) can be constructed using a greedy algorithm: start with the string \(k^n\), and continually append the least symbol possible without repeating a substring of length \(n\). This construction also creates universal cycles for some subsets \(\mathbf{S}\subseteq\mathbf{T}(n,k)\); we will classify all such subsets that are closed under rotations.